Question: A group of adults and kids went to see a movie. Tickets cost $$6.50$ each for adults and $$2.50$ each for kids, and the group paid $$28.00$ in total. There were $4$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Answer: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${6.5x+2.5y = 28}$ ${x = y-4}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-4}$ for $x$ in the first equation. ${6.5}{(y-4)}{+ 2.5y = 28}$ Simplify and solve for $y$ $ 6.5y-26 + 2.5y = 28 $ $ 9y-26 = 28 $ $ 9y = 54 $ $ y = \dfrac{54}{9} $ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into ${x = y-4}$ to find $x$ ${x = }{(6)}{ - 4}$ ${x = 2}$ You can also plug ${y = 6}$ into ${6.5x+2.5y = 28}$ and get the same answer for $x$ ${6.5x + 2.5}{(6)}{= 28}$ ${x = 2}$ There were $2$ adults and $6$ kids.